An Algorithm for Computing Fekete Points in the Triangle
An Algorithm for Computing Fekete Points in the Triangle
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DOI：
10.1137/s0036142998337247
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发表时间：
2000-10
期刊：
影响因子：
--
通讯作者：
Mark A. Taylor;B. Wingate;Rachel E. Vincent
中科院分区：
文献类型：
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作者：
Mark A. Taylor;B. Wingate;Rachel E. Vincent
在直线及其张量积上的Fekete点是Gauss-Lobatto求积点。但与高阶求积不同的是，Fekete点推广到非张量积域，如三角形。因此，Fekete点可以作为替代高斯-洛巴托点的某些应用。在这项工作中，我们提出了一个新的算法来计算Fekete点，并给出结果的程度为19的三角形。对于度d > 10，这些点具有目前已知的最小Lebesgue常数。计算验证了Bos [J. Approx. Theory，64（1991），pp. [271- 280]证明了沿着三角形边界的Fekete点是一维Gauss-Lobatto点。
On the line and its tensor products, Fekete points are known to be the Gauss--Lobatto quadrature points. But unlike high-order quadrature, Fekete points generalize to non-tensor-product domains such as the triangle. Thus Fekete points might serve as an alternative to the Gauss--Lobatto points for certain applications. In this work we present a new algorithm to compute Fekete points and give results up to degree 19 for the triangle. For degree d > 10 these points have the smallest Lebesgue constant currently known. The computations validate a conjecture of Bos [ J. Approx. Theory, 64 (1991), pp. 271--280] that Fekete points along the boundary of the triangle are the one-dimensional Gauss--Lobatto points.